"Things have an amazing way of working out," Mr. Santorum told supporters in Missouri, where he traced his campaign through a series of highs and lows. He called his showing in Kansas a "comfortable win" that would give him the vast majority of the 40 delegates at stake.

In Wyoming, Mr. Romney won seven of the 12 delegates at stake, Mr. Santorum three, Mr. Paul one. Uncommitted also received one.

All four GOP hopefuls had planned to campaign in Kansas. But in a tacit acknowledgment of Mr. Santorum's strength there, both Mr. Romney and Mr. Gingrich decided to bypass the state in favor of campaigning in the South.

That left Mr. Santorum battling on the ground against Mr. Paul, who drew huge crowds of young people in recent days but whose supporters did not materialize in great numbers on Saturday.

The day's events unfolded as the candidates pointed toward Tuesday's primaries in Alabama and Mississippi that loom as unexpectedly important in the race to pick an opponent to President Obama in the fall.

On Tuesday in Alabama and Mississippi, a total of 90 delegates is at stake.

Polls show a close race in both states, particularly Alabama, where Mr. Romney, Mr. Gingrich, and Mr. Santorum all added to their television advertising overnight for the race's final days.

Mr. Gingrich, struggling for survival in the race, can ill afford a loss in either state. Mr. Romney is seeking a Southern breakthrough to demonstrate an ability to win the support of evangelical voters.

For his part, Mr. Santorum hopes to knock Mr. Gingrich out of the race and finally emerge as Mr. Romney's sole challenger from the right.

After primaries or caucuses in 26 states and territories, Mr. Romney holds a commanding lead in delegates. His strategists argue it is all but impossible for any other candidate to capture the 1,144 delegates needed for the nomination.

Mr. Romney, who had 431 delegates going into the caucuses on Saturday, more than all of his rivals combined, picked up an additional nine in Guam on Saturday by a unanimous show of hands among the 215 people eligible to vote at the convention.

He also won nine delegates from the caucus in the Northern Mariana Islands.

The Virgin Islands was also scheduled to caucus on Saturday.

For Mr. Santorum to overtake Mr. Romney, the Romney campaign has argued that he would need to win 65 percent of remaining delegates, a very long shot.

But Mr. Santorum has disputed the math.

He has demanded that delegates awarded to Mr. Romney in the winner-take-all primaries in Florida and Arizona, 79 in all, be split among the candidates, based on Republican National Committee rules. "The RNC is going to be forced to play by the rules whether or not Arizona and Florida want to," Mr. Santorum said on Friday, according to news accounts.

The committee has indicated, however, that it will not force Florida and Arizona to award delegates proportionally.

Santorum supporters are pressing Mr. Gingrich, whose lone victory on Super Tuesday was in Georgia, to drop out to unite conservatives and stop Mr. Romney.

But Mr. Gingrich, whose aides indicated earlier that he would withdraw if he did not win Alabama and Mississippi, now vows to slog his way to the August convention.

"I just want to set this to rest once and for all," Mr. Gingrich said Friday. "We're going to Tampa."

Mr. Paul has also vowed to remain in the race up to the convention, even though he has yet to win a state.

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